Sampling of digital signal values occurs in many applications, such as signal, speech and video processing, high-speed data converters, power spectral estimation, etc. Many signal processing processes or display systems work with substantially uniformly spaced samples; however, at times, substantially nonuniform digital signal samples are available, rather than substantially uniform signal samples.
For nonuniform sampling, if a signal to be sampled is assumed to be sampled nonuniformly and periodically, conventional reconstruction methods may involve use of a filter bank structure. One application addresses timing mismatch in time-interleaved (TI) analog-to-digital converters (ADCs).
Assuming, for example, that timing mismatches in TI ADCs are known and fixed, a synthesis filter bank may potentially be realized using time varying finite impulse response (FIR) filters. See, for example, Eldar Y. C. and Oppenheim A. V., “Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples,” IEEE Trans. Signal Process., vol. 48, no. 10, pp. 2864-2875, October 2000; H. Johansson and P. Löwenborg, “Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters,” IEEE Trans. Signal Process., vol. 50, no. 11, pp. 2757-2767, November 2002; and S. Prendergast, B. C. Levy, and P. J. Hurst, “Reconstruction of bandlimited periodic nonuniformly sampled signals through multirate filter banks,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 51, no. 8, pp. 1612-1622, August 2004. However, issues may arise if time-skew errors change during operation. This may occur for a variety of reasons, such as component aging, temperature variation, or other reasons, for example. A synthesis filter bank may be redesigned to deal with timing mismatch. However, this may involve the use of general-purpose multipliers, which may tend to increase implementation costs, power consumption at high data rates, or have other disadvantages.
Recently, use of more sophisticated digital filters, such as multivariate polynomial impulse response time varying FIR filters, has been proposed to realize a tunable synthesis filter bank See, for example, H. Johansson, P. Lowenborg, and K. Vengattaramane, “Reconstruction of M-periodic nonuniformly sampled signals using multivariate polynomial impulse response time-varying FIR filters,” in Proc. XII Eur. Signal Process. Conf., Florence, Italy, Sep. 4-8, 2006; and S. Huang and B. C. Levy, “Blind calibration of timing offset for four-channel time-interleaved ADCs,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 4, pp. 863-876, April 2006. Time-skew errors for different channels may be included in a synthesis filter bank so that a filter response may be adjusted by several tuning variables. From an implementation point of view, a synthesis filter bank may be implemented without multipliers, except for a limited number of tuning variables, which may be advantageous. While relatively successful with a small number of channels or small range of time-skew errors, otherwise issues may exist. For instance, an M-channel TI ADC generally has at least (M−1) synthesis filters which are functions of M variables. Consequently, a design may become challengingly difficult, as M increases. Moreover, high implementation complexity may be another drawback.
Alternate reconstruction methods that do not use a filter bank structure exist for various classes of nonuniformly sampled signals. For example, iterative methods, such as described in F. Marvasti, M. Analoui, and M. Gamshadzahi, “Recovery of signals from nonuniform samples using iterative methods,” IEEE Trans. Signal Process., vol. 39, pp. 872-877, April 1991, and E. I. Plotkin, M. N. S. Swamy and Y. Yoganandam, “A novel iterative method for the reconstruction of signals from nonuniformly spaced samples,” Signal Process., vol. 37, pp. 203-213, 1994, were commonly used for recovery of nonperiodically sampled signals. However, implementation complexities of these approaches may at times be higher than those of filter banks, making them less attractive in real-time applications, such as TI ADCs. Another disadvantage is a possibility of an ill-behaved system matrix formed by a truncated sinc series, which may result in a relatively low convergence rate or may potentially raise implementation cost.
Another class of parallel ADC arrays called hybrid filter bank (HFB) ADC makes use of analog analysis bank and may be capable of attenuating timing mismatch. See, for example, S. R Velazquez, T. Q. Nguyen and S. R. Broadstone, “Hybrid filter bank analog/digital converter,” U.S. Pat. No. 5,568,142, October 1996. Although performance of HFB ADCs may typically be less sensitive to mismatch than conventional TI ADCs, design of accurate frequency-selective analog analysis filters and sophisticated digital synthesis filters may make implementation more complicated.